Some vertices moving farther than the armature in pose mode/weight paint
The rigging is not good, several bones are controlling the tails so their influence are conflicting.

You can see it if you select your armature, go in Pose mode, then select your mesh and go in Weight Paint mode. Select each bone: the color of the mesh is the influence this bone has on this part of the mesh. The more it's red the more it influences. Blue is zero influence.

You can correct this with the brush (Add or Substract option depending if you want to add or substract weight, and don't forget to enable the vertex selection masking for painting in the bottom horizontal menu).

You can also correct in Edit mode, go in the Properties > Data > Vertex Groups menu and decide, with the vertex group selected and the Assign and Remove buttons, what part of the mesh is supposed to be influence by what bone.



Also, I don't think that the topology of your mesh is good, it is supposed to fit the movements you could make with the bones. For example you can't properly parent each bone of your tail to each segment of your 
mesh as there are no edge loops separating each segments of the mesh.

The best thing for your tail would be to let it as one piece and to parent it to the first bone of your tail: it would control the whole tail and the other bones would be useless, but even this solution is not easy as the tail mesh sticks to the body mesh and the bone would also affect the body. For example it would be easier it the tail was in the same object but a separated mesh.